Topological differences between force-free field models

The potential and linear force-free field models for the magnetic field in the solar corona are often used in the analysis of flares. The field is cal culated using boundary values measured in the low solar atmosphere. The top ology of the field calculated using these models is then compared to the po sition of flare emissions. We demonstrate that the topology of the field ac cording to each of these models, with the same boundary conditions in place , is not in general even qualitatively equivalent. An argument is given for a similar discrepancy between a linear force-free field solution and a non linear force-free field solution.